Firstly the negotiation is due to the available ciphers and the preference of them that your web-browser offers to the site. You'll find that you get different behaviour between Firefox and Chrome on even the same computer for example. SSL was renamed (and updated to) newer TLS versions these days but the information is valid for both.

The cipher suite list, passed from the client to the server in the ClientHello message, contains the combinations of cryptographic algorithms supported by the client in order of the client's preference (favorite choice first). Each cipher suite defines a key exchange algorithm, a bulk encryption algorithm (including secret key length), a MAC algorithm, and a PRF. The server will select a cipher suite or, if no acceptable choices are presented, return a handshake failure alert and close the connection.

But as you explain you are using the same browser on both. So what could be different?

As listed by another user, the browser can choose to make the decision to prioritise one cipher over another for any reason it likes which may be down to power source (battery/mains), amount of CPU resource (mobile/desktop PC) and type of CPU hardware available (offloaded AES for instance?).

On some platforms the TLS is actually passed to the operating system for it to manage and limitations in that platform might limit the available ciphers and options supported. There's a nice list on TechNet under "Cipher suite and protocol support" and Differences in the Schannel SSP by Operating System Version and the best breakdown by Windows OS version is probably here. These can even be different between different patches being installed on the same version of Windows. Microsoft Outlook for instance will negotiate different versions and ciphers based on what version of Windows it is installed on. I wouldn't be surprised if Microsoft Edge and Microsoft Internet Explorer followed a similar pattern.

Finally when you visit a site such as Google.com your request will likely be routed to one of many different servers they have which may be configured differently between requests. Google are known to trial various features by changing options for a small number of users initially and then incrementally increasing so it's not impossible to think they might return back with support for some new ciphers one month that they didn't support before and slowly allow more connections to use them.